Given $ m \angle LOM = 5x + 40$, and $ m \angle MON = 8x - 55$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {5x + 40} + {8x - 55} = {180}$ Combine like terms: $ 13x - 15 = 180$ Add $15$ to both sides: $ 13x = 195$ Divide both sides by $13$ to find $x$ $ x = 15$ Substitute $15$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 5({15}) + 40$ Simplify: $ {m\angle LOM = 75 + 40}$ So ${m\angle LOM = 115}$.